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Simplifying b3 + -6b2 + -6b = 0 Reorder the terms: -6b + -6b2 + b3 = 0 Solving -6b + -6b2 + b3 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), 'b'. b(-6 + -6b + b2) = 0Subproblem 1
Set the factor 'b' equal to zero and attempt to solve: Simplifying b = 0 Solving b = 0 Move all terms containing b to the left, all other terms to the right. Simplifying b = 0Subproblem 2
Set the factor '(-6 + -6b + b2)' equal to zero and attempt to solve: Simplifying -6 + -6b + b2 = 0 Solving -6 + -6b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + -6b + 6 + b2 = 0 + 6 Reorder the terms: -6 + 6 + -6b + b2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -6b + b2 = 0 + 6 -6b + b2 = 0 + 6 Combine like terms: 0 + 6 = 6 -6b + b2 = 6 The b term is -6b. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6b + 9 + b2 = 6 + 9 Reorder the terms: 9 + -6b + b2 = 6 + 9 Combine like terms: 6 + 9 = 15 9 + -6b + b2 = 15 Factor a perfect square on the left side: (b + -3)(b + -3) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (b + -3) equal to 3.872983346 and -3.872983346.Subproblem 1
b + -3 = 3.872983346 Simplifying b + -3 = 3.872983346 Reorder the terms: -3 + b = 3.872983346 Solving -3 + b = 3.872983346 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + b = 3.872983346 + 3 Combine like terms: -3 + 3 = 0 0 + b = 3.872983346 + 3 b = 3.872983346 + 3 Combine like terms: 3.872983346 + 3 = 6.872983346 b = 6.872983346 Simplifying b = 6.872983346Subproblem 2
b + -3 = -3.872983346 Simplifying b + -3 = -3.872983346 Reorder the terms: -3 + b = -3.872983346 Solving -3 + b = -3.872983346 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + b = -3.872983346 + 3 Combine like terms: -3 + 3 = 0 0 + b = -3.872983346 + 3 b = -3.872983346 + 3 Combine like terms: -3.872983346 + 3 = -0.872983346 b = -0.872983346 Simplifying b = -0.872983346Solution
The solution to the problem is based on the solutions from the subproblems. b = {6.872983346, -0.872983346}Solution
b = {0, 6.872983346, -0.872983346}
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